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a) (-124) + 24 = -100
b) 37. 78 + 37. 22
= 37 . ( 78 + 22 )
= 37 . 100
= 3700
a) \(\dfrac{7}{30}+\dfrac{\left(-12\right)}{37}+\dfrac{23}{30}+\dfrac{\left(-25\right)}{37}=\left(\dfrac{7}{30}+\dfrac{23}{30}\right)+\left(\dfrac{-12}{37}+\dfrac{-25}{37}\right)=1+\left(-1\right)=0\)
b) \(\dfrac{5}{7}\cdot\dfrac{5}{11}+\dfrac{5}{7}\cdot\dfrac{2}{11}-\dfrac{5}{7}\cdot\dfrac{14}{11}=\dfrac{5}{7}\cdot\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)=\dfrac{5}{7}\cdot\left(-\dfrac{7}{11}\right)=-\dfrac{5}{11}\)
c) \(\dfrac{\left(-5\right)}{7}\cdot\dfrac{3}{13}-\dfrac{5}{7}\cdot\dfrac{10}{13}+1\dfrac{5}{7}=\dfrac{5}{7}\cdot\dfrac{-3}{13}-\dfrac{5}{7}\cdot\dfrac{10}{13}+\dfrac{12}{7}=\dfrac{5}{7}\cdot\left(\dfrac{-3}{13}-\dfrac{10}{13}\right)+\dfrac{12}{7}=\dfrac{5}{7}\cdot\left(-1\right)+\dfrac{12}{7}=\left(-\dfrac{5}{7}\right)+\dfrac{12}{7}=\dfrac{7}{7}=1\)
8 − 9 4 + 2 7 − − 6 − 3 7 + 5 4 − 3 + 2 4 − 9 7 = 8 − 9 4 + 2 7 + 6 + 3 7 − 5 4 − 3 − 2 4 + 9 7 = 8 + 6 − 3 − 9 4 − 5 4 − 2 4 + 2 7 + 3 7 + 9 7 = 11 − 4 + 2 = 9
= 37 x 27 - 27 x 13 - 27 x 37 - 27 x 13
= 27 x ( 37 - 37 - 13 - 13 )
= 27 x 0
= 0